The “Barn Paradox”
A runner, travelling at 0.75c (!!), is carrying a long pole, which he knows to have length
15m. The pole is oriented in his direction of travel. He carries the pole as he passes through
a barn, which has a length of 10 m.
Straightforward . . . so what is the paradox?
•
The length of the pole as measured by an observer who is stationary with respect to
the ground is 9.9m.
This is an application of “length contraction”.
Thus, the pole seems shorter to the
observer on the ground, because it is moving in his frame of reference. The length that
he observes is
L
=
L
0
/γ
15
/
1
.
51
9
.
9
m
because
γ
=
q
16
/
7
1
.
51
.
Thus, according to the observer, when the runner enters the barn (whose length, measured
with respect to the ground, is 10m), the pole should be able to fit inside!
Now the paradox:
•
The length of the barn as seen (measured) by the runner is 6.6m.
This is again an example of “length contraction”.
In the frame of reference of the
runner, the barn is moving, so that its length is measured to be
L
B
=
L
B
/γ
10
/
1
.
51
6
.
6
m
How then
can
the pole fit inside?
To explain, imagine that there are two doors to the barn, one for the entry, and one for
the exit of the runner. (He is always running in a straight line.) At the beginning, the entry
door is open, but the exit door is closed. Exactly at the time that the pole fits inside, the
entry door closes, and the exit door opens, to allow the pole to pass through. These two
events – closing the entry door and opening the exit door – happen, in this frame, at exactly
the same time.
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 Fall '07
 Harris
 Special Relativity, Frame of reference, Spacetime, Pole, Exit Door, entry door

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